On Generalized Monopole Spherical Harmonics and the Wave Equation of a Charged Massive Kerr Black Hole

TL;DR

This paper derives generalized monopole spherical harmonics as solutions to the Goncharov-Firsova equation for a massive scalar field around a Kerr black hole, extending classical solutions to include mass effects.

Contribution

It introduces a new class of solutions for the Goncharov-Firsova equation that incorporate mass, broadening the understanding of scalar fields in Kerr black hole backgrounds.

Findings

Derived linearly independent solutions for massive scalar fields.

Extended classical monopole harmonics to include mass effects.

Provides mathematical tools for analyzing massive fields in black hole spacetimes.

Abstract

We find linearly independent solutions of the Goncharov-Firsova equation in the case of a massive complex scalar field on a Kerr black hole. The solutions generalize, in some sense, the classical monopole spherical harmonic solutions previously studied in the massless cases.